Sommerfeld Effect Research Articles

Determining experimentally the patterns of the manifestation of the Sommerfeld effect in a ball auto-balancer

This paper proposes an experimental method for studying the Sommerfeld effect in auto-balancers or exciters of resonant vibrations of pendulum, ball, or roller type. The method is based on the processing of signals acquired from analog sensors of rotations and vibration acceleration using regression analysis. The method is tested on a specially designed rotor bench on isotropic viscoelastic supports, which executes spatial motion, and an auto-balancer with one ball. Checking the accuracy of the method using stroboscopic lighting demonstrates the accuracy of determining the speed of rotation of the rotor, ball, oscillation frequency of the rotor, etc. with an error of several hundredths of a percent. When fixing the ball relative to the rotor, a classic inertial vibration exciter is obtained. The rotor has two resonant velocities. The Sommerfeld effect is almost not manifested. With a gradual increase in the frequency of the current, the rotor speed increases monotonously. There is no significant slip or jump in the rotor speed. There are two distinct peaks on the amplitude-frequency characteristic. Therefore, such a vibration exciter is not suitable for the excitation of resonant vibrations. With the free placement of the ball in the oil, the behavior of the system changes significantly in the vicinity of the first resonant velocity. The first narrow resonant peak disappears in the roto. Instead, there is a long, gentle resonant rise. It lasts at a current frequency of 9.4 Hz to 19.3 Hz. The amplitude at the reference point on the resonant rise increases from 0.7 mm to 2.84 mm. Therefore, by changing the frequency of the current, it is possible to smoothly change the amplitude of the rotor oscillations by almost 4 times. The maximum amplitude of rotor oscillations is the same as at the first resonance with a fixed ball. Due to the gentleness of the resonant rise, a freely installed ball itself is a reliable exciter of resonant vibrations

Impact of Sommerfeld effect and bound state formation in simplified t-channel dark matter models

The existence of a dark matter model with a rich dark sector could be the reason why WIMP dark matter has evaded its detection so far. For instance, colored coannihilation naturally leads to the prediction of heavier dark matter masses. Importantly, in such a scenario the Sommerfeld effect and bound state formation must be considered in order to accurately predict the relic abundance. Based on the example of the currently widely studied t-channel simplified model with a colored mediator, we demonstrate the importance of considering these non-perturbative effects for correctly inferring the viable model parameters. We emphasize that a flat correction factor on the relic abundance is not sufficient in this context. Moreover, we find that parameter space thought to be excluded by direct detection experiments and LHC searches remains still viable. Additionally, we illustrate that long-lived particle searches and bound-state searches at the LHC can play a crucial role in probing such a model. We demonstrate how future direct detection experiments will be able to close almost all of the remaining window for freeze-out production, making it a highly testable scenario.

A Theoretical Approach for Resonance Analysis of Wind Turbines under 1P/3P Loads

Wind turbines (WTs) are exposed to a dynamic/cyclic load environment, and are subjected to 1P/3P loads under operational conditions. Recent studies introduced the Sommerfeld Effect to explain the dynamic response amplification induced by 1P/3P loads. This study establishes a theoretical model to analyze the resonance of WTs under 1P/3P loads. Sensitiveness analysis was conducted for parameters b, c, S, F, and T to explore their influence on the dynamic response. The resonance phenomenon induced by 1P/3P frequency passing the natural frequency is discussed. The results show that there is no Sommerfeld Effect in soft–stiff WTs. Only if the imbalance reaches a much higher value (19200 kg·m in this study) should the Sommerfeld Effect be considered for soft WTs; otherwise, it can be ignored. The 3P resonance appeared when the 3P frequency approached the natural frequency, but it was not the Sommerfeld Effect.

A new approach to suppressing the Sommerfeld effect in vibrating structures

A new approach to suppressing the Sommerfeld effect in vibrating structures

Final bound-state formation effect on dark matter annihilation * *Supported in part by the One Hundred Talent Program of Sun Yat-sen University, China

If two annihilation products of dark matter (DM) particles are non-relativistic and couple to a light force mediator, their plane wave functions are modified due to multiple exchanges of the force mediator. This gives rise to the final state Sommerfeld (FSS) effect. It is also possible that the final state particles form a bound state. Both the FSS effect and final bound-state (FBS) effect need to be considered in the calculation of the DM relic abundance. The annihilation products can be non-relativistic if their masses are comparable to those of the annihilating DM particles. We study the FSS and FBS effects in the mass-degenerate region using two specific models. Both models serve to illustrate different partial-wave contributions in the calculations of the FSS and FBS effects. We find that the FBS effect can be comparable to the FSS effect when the annihilation products couple strongly with a light force mediator. Those effects significantly modify the DM relic abundance.

Dynamic modeling of a non-ideal gyroscopic rotor system with nonlinear damping and nonlinear rigidity of an elastic support

The article considers the effect of joint linear and nonlinear cubic damping on dynamics of a gyroscopic rigid rotor interacting with an electric motor with a rectilinear characteristic, taking into account the nonlinear rigidity of the support material. The method of regulating the control parameter (voltage on the motor), the amplitude of vibration, and the angular velocity of the shaft in the frequency equation, depending on the value of the coefficient of nonlinear cubic damping of the support, offers the most effective options for controlling resonant oscillations of large amplitudes. It is shown that the greater the value of the coefficient of nonlinear cubic damping, the easier it is to control these oscillations. Moreover, it is proved that the Sommerfeld effect (of the first kind) can also be weakened and eliminate with the help of joint linear and nonlinear damping. To do this, in the case of a rigid characteristic of the nonlinear elasticity of the support material, in a rotor system with a nonideal energy source to eliminate the bistability region, that is, jumping effects, more nonlinear damping of support or energy from a nonideal energy source will be required than in the case of an ideal rotor system.

Time‐varying piecewise nonlinear dynamic model of the vibrating machinery with elliptical trajectory consider the interactions between its frame and particles

AbstractVibrating machinery with an elliptical trajectory widely exists. The bulk particles show a regular sliding motion and throwing motion under the periodic vibration of the frame. It is essential for the theoretical design and engineering application of such machinery to study the particle's motion theory based on considering the interactions between particles and frame in detail. In the first, a time‐varying piecewise nonlinear dynamic model of the system is established based on the force analysis of the particles in the state of sliding and throwing motion. The dimensionless equations of systems with nonlinear terms are deduced. After that, the feasibility of using a single particle to study the particle flow's movement is verified by the discrete element method. Then, the system's approximate steady‐state analytical solution is obtained by the incremental harmonic balance method. Its numerical solutions are solved by the Newmark‐β method, and the solutions obtained by the three methods are verified mutually. In addition, the Sommerfeld effect in vibration system and the system's related parameters are analyzed. Finally, an experimental platform of particles' movement is built. The feasibility of the theoretical analysis in this article was verified by particle's movement experiments.

Matching resummed endpoint and continuum γ-ray spectra from dark-matter annihilation

For the minimal wino and Higgsino benchmark models we provide accurate energy spectra of high-energy photons from TeV scale dark-matter annihilation χχ→γ+X by merging electroweak Sudakov resummation near maximal energy with the electroweak parton-shower PPPC4DM, and accounting for the Sommerfeld effect. Electroweak resummation significantly changes the shape of the photon-energy spectrum in the wide range Eγ∼(0.6…1)mχ and hence the form of the so-called “line-signal”.

Electroweak dark matter

In the absence of any hints of new physics in LHC, TeV dark matter candidates interacting through electroweak force (EWDM) are still highly motivated. We extend the Standard Model by adding an arbitrary SU(2) DM multiplet in non-chiral representation. In addition to the well-known real representation which has no coupling to the nuclei at tree level, the complex representation can lead to a new DM candidate providing that one includes a higher dimensional mass-splitting operator, which survives the current direct detection bounds. Since the masses of gauge mediators are light compared to the dark particles, Sommerfeld effect is dominant and affects the value of annihilation cross-section in both the early universe and current time. We computed the relic abundance through freeze-out mechanism in order to determine DM mass. Gamma ray fluxes in our galaxy and dwarf satellites provide a promising tool to probe EWDM theory. We confronted the four fermionic representations of the model with the latest astrophysical observations. It can be concluded that the model passes the current experimental constraints successfully, and it is accessible to future observations.

Instability attenuation and bifurcation studies of a non-ideal rotor involving time-delayed feedback

In non-ideal vibratory system, the excitation is a nonlinear function of system response. The dynamic behavior of such system is often characterized by an energy source with limited power. The study of instability phenomena in non-ideal rotor driven through a non-ideal energy source is of considerable current interest. The non-ideal rotor system often gets destabilized on exceeding a critical input power near the resonance. This kind of instability is termed as Sommerfeld effect marked with nonlinear jump phenomena. This paper investigates the attenuation of nonlinear jump phenomena and numerical study of bifurcations of a non-ideal unbalanced rotor system with internal damping using time-delayed feedback via active magnetic bearings. The results show that the time delay indeed plays a critical role on the suppression of the jump phenomena. Following, some new insights are also revealed through a numerical study of saddle node, Hopf and trans-critical bifurcations with time delay as a bifurcation parameter. The transient analysis confirms the results obtained analytically through the steady-state consideration.

Dynamics of a resonant vibrator with an equal-frequency suspension of the working body and an unbalanced vibration exciter

The article studies the dynamics of resonant vibration machines with a variable mass of the material processed, used in vibrational transportation, screening, compaction, etc. The main purpose of the work was to substantiate the use of nonlinear elastic elements as a suspension of the working bodies of vibration machines with unbalanced vibration exciters to ensure a constant resonant excitation frequency at various system mass values. The design circuit consisted of a single-mass vibration machine in the form of a system with a concentrated mass, mounted on a nonlinear elastic spring performing rectilinear oscillations in the field of gravitational forces. The static characteristic of the unbalanced vibration exciter motor was taken into account, leading to a nonlinear interaction of the working body and the unbalanced vibrator due to the presence of an imperfect energy source in the system. The supply voltage of the electric motor was taken as the control parameter. Based on Lagrange equations of the second kind, a system of differential equations has been developed that describes respective system motion depending on the mass of the material being processed. The amplitude and frequency characteristics were established depending on the power supply voltage of the electric motor and the average rpm of the unbalance for various material mass values. A manifestation of the Sommerfeld effect was observed. The constancy of the resonance amplitude and vibration frequency of the working body of the vibration machine on an equal-frequency suspension at various load mass values has been shown.The study was carried out under grant No. 21-19-00183 issued by the Russian Science Foundation.

Speed Oscillations of a Vehicle Rolling on a Wavy Road

Every driver knows that his car is slowing down or accelerating when driving up or down, respectively. The same happens on uneven roads with plastic wave deformations, e.g., in front of traffic lights or on nonpaved desert roads. This paper investigates the resulting travel speed oscillations of a quarter car model rolling in contact on a sinusoidal and stochastic road surface. The nonlinear equations of motion of the vehicle road system leads to ill-conditioned differential-algebraic equations. They are solved introducing polar coordinates into the sinusoidal road model. Numerical simulations show the Sommerfeld effect, in which the vehicle becomes stuck before the resonance speed, exhibiting limit cycles of oscillating acceleration and speed, which bifurcate from one-periodic limit cycle to one that is double periodic. Analytical approximations are derived by means of nonlinear Fourier expansions. Extensions to more realistic road models by means of noise perturbation show limit flows as bundles of nonperiodic trajectories with periodic side limits. Vehicles with higher degrees of freedom become stuck before the first speed resonance, as well as in between further resonance speeds with strong vertical vibrations and longitudinal speed oscillations. They need more power supply in order to overcome the resonance peak. For small damping, the speeds after resonance are unstable. They migrate to lower or supercritical speeds of operation. Stability in mean is investigated.

Dynamic characteristics of a simply supported elastic beam with three induction motors

In the paper, the dynamic characteristics of a three induction motor driven system on a simply supported elastic beam are studied. Firstly, a dynamic coupling model of the whole system is established according to the Hamilton principle and discretized by applying the assumed mode method. Next, the synchronization solutions containing the average rotation speeds and phase differences of three motors and their stability are calculated and analyzed by using the average perturbation method. As a result, the synchronization and stability conditions of self-synchronization of three motors are established. Finally, the feasibility of the average perturbation method is verified by comparing the theoretical results with the simulation results. The results indicate that the elastic support has a large influence on the motion states of three motors. There is the self-synchronization phenomenon of three motors on the elastic beam. There appear the Sommerfeld effect (rotational speed capture and jump phenomena) near the resonance of the beam and the synchronous states of three motors will rapidly change before and after the resonance of beam. The large changes of the motion states of three motors cause the impacts of the responses of the elastic beam structure. Additionally, the effects of the structure parameters such as unbalance mass, power frequency, beam size and vibration modes on the dynamic characteristics of the system are discussed. This paper can provide some references for the design of multi-motor systems on the elastic foundations.

Modelling and Simulation of Nonlinear Jump Phenomena of a Non-ideal Rotor Involving Fractional Order PD Controller

Rotating machinery with high speed powered by industrial motors frequently suffers from instability by exhibiting non-linear jump phenomena, formally known as Sommerfeld effect. The drives whose excitation is a function of the system responses, referred to as non-ideal. The system dynamics of such systems exhibit a couple of complex and interesting features when the input power exceeds a critical value. The present research suggests a novel approach to study the efficacy of active magnetic bearing with fractional PD controller to suppress the instability caused by the Sommerfeld effect. The steady-state results obtained by solving the system characteristic equation numerically is compared with the transient analysis. Finally, root locus method is introduced to obtain the bifurcation points at which this kind of instability completely disappears.

Determining the energy efficiency of a resonance single-mass vibratory machine whose operation is based on the Sommerfeld effect

This paper reports determining the energy efficiency of a vibratory machine consisting of a viscoelastically fixed platform that can move vertically, and a vibration exciter whose operation is based on the Sommerfeld effect. The body of the vibration exciter rotates at a steady angular speed while there are the same loads in the form of a ball, a roller, or a pendulum inside it. The load, being moved relative to the body, is exposed to the forces of viscous resistance, which are internal within the system. It was established that under the steady oscillatory modes of a vibratory machine's movement, the loads are tightly pressed to each other, thereby forming a combined load. Energy is productively spent on platform oscillations and unproductively dissipated due to the movement of the combined load relative to the body. With an increase in the speed of the body rotation, the increasing internal forces of viscous resistance bring the speed of rotation of the combined load closer to the resonance speed, and the amplitude of platform oscillations increases. However, the combined load, in this case, increasingly lags behind the body, which increases unproductive energy loss and decreases the efficiency of the vibratory machine. A purely resonant motion mode of the vibratory machine produces the maximum amplitude of platform oscillations, the dynamic factor, the total power of viscous resistance forces. In this case, the efficiency reaches its minimum value. To obtain vigorous oscillations of the platform with a simultaneous increase in the efficiency of the vibratory machine, it is necessary to reduce the forces of viscous resistance in supports with a simultaneous increase in the internal forces of viscous resistance. An algorithm for calculating the basic dynamic characteristics of the vibratory machine's oscillatory motion has been built, based on solving the problem parametrically. The accepted parameter is the angular speed at which a combined load gets stuck. The effectiveness of the algorithm has been illustrated using a specific example

A Short Note on Synchrosqueezed Transforms for Resonant Capture, Sommerfeld Effect and Nonlinear Jump Characterization in Mechanical Systems

A Short Note on Synchrosqueezed Transforms for Resonant Capture, Sommerfeld Effect and Nonlinear Jump Characterization in Mechanical Systems

Leptophilic-portal dark matter in the light of AMS-02 positron excess

We revisit dark matter annihilation as an explanation of the positron excess reported recently by the AMS-02 satellite-borne experiment. To this end, we propose a particle dark matter model by considering a Two Higgs Doublet Model (2HDM) extended with an additional singlet boson and a singlet fermion. The additional (light) boson mixes with the pseudoscalar inherent in the 2HDM, and the singlet fermion, which is the dark matter candidate, annihilates via this bosonic portal. The dark matter candidate is made leptophilic by choosing the lepton-specific 2HDM and a suitable high value of $\tan\beta$. We identify the model parameter space which explains the muon g-2 anomaly while evading the experimental constraints. After establishing the viability of the singlet fermion to be a dark matter candidate, we calculate the positron excess produced from its annihilation to the light bosons which primarily decay to muons. Incorporating the Sommerfeld effect caused by the light mediator and an appropriate boost factor, we find that our proposed model can satisfactorily explain the positron fraction excess as well as the positron spectrum data reported by AMS-02 experiment.

Thermal real scalar triplet dark matter

Real scalar triplet dark matter, which is known to be an attractive candidate for a thermal WIMP, is comprehensively studied paying particular attention to the Sommerfeld effect on the dark matter annihilation caused by the weak interaction and the other interaction between the dark matter and the Higgs boson. We find a parameter region that includes the so-called ‘WIMP-Miracle’ one is still surviving, i.e. it respects all constraints imposed by dark matter searches at collider experiments, underground experiments (direct detection) and astrophysical observations (indirect detection). The region is also found to be efficiently searched for by various near future experiments. In particular, the XENONnT experiment will cover almost the entire parameter region.

Sommerfeld-enhanced dark matter searches with dwarf spheroidal galaxies

We study observable signals from dark matter that self-annihilates via the Sommerfeld effect in dwarf spheroidal galaxies (dSphs). Since the effect of the Sommerfeld enhancement depends on the velocity of dark matter, it is crucial to determine the profile of dSphs to compute the J-factor, i.e., the line-of-sight integral of density squared. In our study we use the prior distributions of the parameters for satellite density profiles in order to determine the J-factor, making most out of the recent developments in the N-body simulations and semi-analytical modeling for the structure formation. As concrete models, we analyze fermionic dark matter that annihilates via a light scalar and Wino dark matter in supersymmetric models. We find that, with the more realistic prior distributions that we adopt in this study, the J-factor of the most promising dSphs is decreased by a factor of a few, compared with earlier estimates based on non-informative priors. Nevertheless, the Cherenkov Telescope Array should be able to detect the thermal Wino dark matter by pointing it toward best classical or ultrafaint dSphs for 500 hours.

The dynamics of a resonance single-mass vibratory machine with a vibration exciter of targeted action that operates on the Sommerfeld effect

This paper reports a study into the dynamics of a vibratory machine composed of a viscoelastically-fixed platform that can move vertically and two identical inertial vibration exciters. The vibration exciters' bodies rotate at the same angular velocities in opposite directions. The bodies host a single load in the form of a ball, roller, or pendulum. The loads' centers of mass can move relative to the bodies in a circle with a center on the axis of rotation. The loads' relative movements are hindered by the forces of viscous resistance. It was established that a vibratory machine theoretically possesses the following: – one to three oscillatory modes of movement under which loads get stuck at almost constant angular velocity and generate total unbalanced mass in the vertical direction only; – a no-oscillation mode under which loads rotate synchronously with the bodies and generate total unbalanced mass in the horizontal direction only. At the same time, only one oscillatory mode is resonant and exists at the above-the-resonance speeds of body rotation, lower than some characteristic speed. At the bodies' rotation speeds: ‒ pre-resonant; there is a globally asymptotically stable (the only existing) mode of load jams; ‒ above-the-resonance, lower than the characteristic velocity; there are locally asymptotically stable regimes ‒ both the resonance mode of movement of a vibratory machine and a no-oscillations mode; ‒ exceeding the characteristic velocity: there is a globally asymptotically stable no-oscillations mode. Computational experiments have confirmed the results of theoretical research. At the same time, it was additionally established that it would suffice, to enter a resonant mode of movement, to slowly accelerate the bodies of vibration exciters to the above-the-resonance speed, less than the characteristic speed. The results reported here could be interesting both for the theory and practice of designing new vibratory machines